Formules pour les espaces multisécants aux courbes algébriques

We give a general new algorithm to find formulas for the number of k-secant d-planes to a smooth curve in PN(C), for any k, d, N. Partial results were given by Castelnuovo [Rend. Palermo 3 (1889) 27-37] and Tanturri [Ann. Mat. 4 (1900) 67-122]. See also E. Arbarello et al. [Geometry of Algebraic Curves, vol. 1, Grundlehren Math. Wiss., vol. 267, Springer-Verlag, 1985]. To cite this article: P. Le Barz, C. R. Acad. Sci. Paris, Ser. I 340 (2005).